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Saturation, HSaturation

Syntax

Saturation(I:IDEAL,J:IDEAL):IDEAL
HSaturation(I:IDEAL,J:IDEAL):IDEAL
    

Summary

saturation of ideals

Description

These functions return the saturation of I with respect to J: the ideal of polynomials F such that FG is in I for all G in J^d for some positive integer d.

The function HSaturation calculates the saturation using a Hilbert-driven algorithm. It differs from Saturation only when the input is inhomogeneous, in which case, HSaturation may be faster.

The coefficient ring must be a field.

example

    
Use R ::= Q[xyz];
I := Ideal(x-z,y-2z);
J := Ideal(x-2z,y-z);
K := Intersection(I,J); -- ideal of two points in the
                        -- projective plane
L := Intersection(K,Ideal(x,y,z)^3); -- add an irrelevant component
Hilbert(R/L);
H(0) = 1
H(1) = 3
H(2) = 6
H(t) = 2   for t >= 3
-------------------------------
Saturation(L,Ideal(x,y,z)) = K; -- saturating gets rid of the
                                -- irrelevant component
TRUE
-------------------------------
        
    

See Also